Typically with these games, you have little time to think. Some players will be operating purely on instinct. The rapid movements they make is where the name comes from. The player will be twitching as they operate the controls.

John: Damn, I thought I was good at Tekken and then I played that Japanese kid.
Sally: He doesn't do anything but drink Jolt Cola, play that game and sleep. He's a twitcher.

When a fully grown man says he has a vagina and when you turn round he has forced ball n all through his legs just leaving his pubic region visible, we all laugh.
If he were then to turn round, open his legs and force his penis back in the opposite to natural direction (his genitals would now be upside down,balls on top) and repeat in quick succession. His manhood would be twitching and therefore making him a Twitcher.